Identifying Logical Planes Formed Of Compute Nodes Of A Subcommunicator In A Parallel Computer

ABSTRACT

In a parallel computer, a plurality of logical planes formed of compute nodes of a subcommunicator may be identified by: for each compute node of the subcommunicator and for a number of dimensions beginning with a first dimension: establishing, by a plane building node, in a positive direction of the first dimension, all logical planes that include the plane building node and compute nodes of the subcommunicator in a positive direction of a second dimension, where the second dimension is orthogonal to the first dimension; and establishing, by the plane building node, in a negative direction of the first dimension, all logical planes that include the plane building node and compute nodes of the subcommunicator in the positive direction of the second dimension.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with Government support under Contract No.B554331 awarded by the Department of Energy. The Government has certainrights in this invention.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The field of the invention is data processing, or, more specifically,methods, apparatus, and products for identifying a plurality of logicalplanes formed of compute nodes of a subcommunicator in a parallelcomputer.

2. Description of Related Art

The development of the EDVAC computer system of 1948 is often cited asthe beginning of the computer era. Since that time, computer systemshave evolved into extremely complicated devices. Today's computers aremuch more sophisticated than early systems such as the EDVAC. Computersystems typically include a combination of hardware and softwarecomponents, application programs, operating systems, processors, buses,memory, input/output devices, and so on. As advances in semiconductorprocessing and computer architecture push the performance of thecomputer higher and higher, more sophisticated computer software hasevolved to take advantage of the higher performance of the hardware,resulting in computer systems today that are much more powerful thanjust a few years ago.

Parallel computing is an area of computer technology that hasexperienced advances. Parallel computing is the simultaneous executionof the same task (split up and specially adapted) on multiple processorsin order to obtain results faster. Parallel computing is based on thefact that the process of solving a problem usually can be divided intosmaller tasks, which may be carried out simultaneously with somecoordination.

Parallel computers execute parallel algorithms. A parallel algorithm canbe split up to be executed a piece at a time on many differentprocessing devices, and then put back together again at the end to get adata processing result. Some algorithms are easy to divide up intopieces. Splitting up the job of checking all of the numbers from one toa hundred thousand to see which are primes could be done, for example,by assigning a subset of the numbers to each available processor, andthen putting the list of positive results back together. In thisspecification, the multiple processing devices that execute theindividual pieces of a parallel program are referred to as ‘computenodes.’ A parallel computer is composed of compute nodes and otherprocessing nodes as well, including, for example, input/output (‘I/O’)nodes, and service nodes.

Parallel algorithms are valuable because it is faster to perform somekinds of large computing tasks via a parallel algorithm than it is via aserial (non-parallel) algorithm, because of the way modern processorswork. It is far more difficult to construct a computer with a singlefast processor than one with many slow processors with the samethroughput. There are also certain theoretical limits to the potentialspeed of serial processors. On the other hand, every parallel algorithmhas a serial part and so parallel algorithms have a saturation point.After that point adding more processors does not yield any morethroughput but only increases the overhead and cost. Parallel algorithmsare designed also to optimize one more resource the data communicationsrequirements among the nodes of a parallel computer. There are two waysparallel processors communicate, shared memory or message passing.Shared memory processing needs additional locking for the data andimposes the overhead of additional processor and bus cycles and alsoserializes some portion of the algorithm.

Message passing processing uses high-speed data communications networksand message buffers, but this communication adds transfer overhead onthe data communications networks as well as additional memory need formessage buffers and latency in the data communications among nodes.Designs of parallel computers use specially designed data communicationslinks so that the communication overhead will be small but it is theparallel algorithm that decides the volume of the traffic.

Many data communications network architectures are used for messagepassing among nodes in parallel computers. Compute nodes may beorganized in a network as a ‘torus’ or ‘mesh,’ for example. Also,compute nodes may be organized in a network as a tree. A torus networkconnects the nodes in a three-dimensional mesh with wrap around links.Every node is connected to its six neighbors through this torus network,and each node is addressed by its x,y,z coordinate in the mesh. In sucha manner, a torus network lends itself to point to point operations. Ina tree network, the nodes typically are connected into a binary tree:each node has a parent, and two children (although some nodes may onlyhave zero children or one child, depending on the hardwareconfiguration). Although a tree network typically is inefficient inpoint to point communication, a tree network does provide high bandwidthand low latency for certain collective operations, message passingoperations where all compute nodes participate simultaneously, such as,for example, an allgather operation. In computers that use a torus and atree network, the two networks typically are implemented independentlyof one another, with separate routing circuits, separate physical links,and separate message buffers.

SUMMARY OF THE INVENTION

Methods, apparatus, and products for identifying a plurality of logicalplanes formed of compute nodes of a subcommunicator in a parallelcomputer are disclosed. Identifying such logical planes may be carriedout, for each compute node of the subcommunicator and for a plurality ofdimensions beginning with a first dimension by establishing, by a planebuilding node, in a positive direction of the first dimension, alllogical planes that include the plane building node and compute nodes ofthe subcommunicator in a positive direction of a second dimension, wherethe second dimension is orthogonal to the first dimension; andestablishing, by the plane building node, in a negative direction of thefirst dimension, all logical planes that include the plane building nodeand compute nodes of the subcommunicator in the positive direction ofthe second dimension.

The foregoing and other objects, features and advantages of theinvention will be apparent from the following more particulardescriptions of exemplary embodiments of the invention as illustrated inthe accompanying drawings wherein like reference numbers generallyrepresent like parts of exemplary embodiments of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an exemplary system for identifying a plurality oflogical planes formed of compute nodes of a subcommunicator in aparallel computer according to embodiments of the present invention.

FIG. 2 sets forth a block diagram of an example compute node of aparallel computer configured for identifying a plurality of logicalplanes formed of compute nodes of a subcommunicator in a parallelcomputer according to embodiments of the present invention.

FIG. 3A sets forth a block diagram of an example Point-To-Point Adapteruseful in systems for identifying a plurality of logical planes formedof compute nodes of a subcommunicator in a parallel computer accordingto embodiments of the present invention.

FIG. 3B sets forth a block diagram of an example Global CombiningNetwork Adapter useful in systems for identifying a plurality of logicalplanes formed of compute nodes of a subcommunicator in a parallelcomputer according to embodiments of the present invention.

FIG. 4 sets forth a line drawing illustrating an example datacommunications network optimized for point-to-point operations useful insystems capable of identifying a plurality of logical planes formed ofcompute nodes of a subcommunicator in a parallel computer according toembodiments of the present invention.

FIG. 5 sets forth a line drawing illustrating an example globalcombining network useful in systems capable of identifying a pluralityof logical planes formed of compute nodes of a subcommunicator in aparallel computer according to embodiments of the present invention.

FIG. 6 sets forth a flow chart illustrating an example method foridentifying a plurality of logical planes formed of compute nodes of asubcommunicator in a parallel computer according to embodiments of thepresent invention.

FIG. 7 sets forth a line drawing illustrating an example communicatorand subcommunicator from which a plurality of logical planes formed ofcompute nodes of the subcommunicator may be identified according toembodiments of the present invention.

FIG. 8A sets forth a line drawing illustrating another examplecommunicator and subcommunicator from which a plurality of logicalplanes formed of compute nodes of the subcommunicator may be identifiedaccording to embodiments of the present invention.

FIG. 8B sets forth a line drawing illustrating another examplecommunicator and subcommunicator from which a plurality of logicalplanes formed of compute nodes of the subcommunicator may be identifiedaccording to embodiments of the present invention.

FIG. 9A sets forth a line drawing illustrating another examplecommunicator and subcommunicator from which a plurality of logicalplanes formed of compute nodes of the subcommunicator may be identifiedaccording to embodiments of the present invention.

FIG. 9B sets forth a line drawing illustrating another examplecommunicator and subcommunicator from which a plurality of logicalplanes formed of compute nodes of the subcommunicator may be identifiedaccording to embodiments of the present invention.

FIG. 10A sets forth a line drawing illustrating another examplecommunicator and subcommunicator from which a plurality of logicalplanes formed of compute nodes of the subcommunicator may be identifiedaccording to embodiments of the present invention.

FIG. 10B sets forth a line drawing illustrating another examplecommunicator and subcommunicator from which a plurality of logicalplanes formed of compute nodes of the subcommunicator may be identifiedaccording to embodiments of the present invention.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

Exemplary methods, apparatus, and products for identifying a pluralityof logical planes formed of compute nodes of a subcommunicator in aparallel computer in accordance with the present invention are describedwith reference to the accompanying drawings, beginning with FIG. 1. FIG.1 illustrates an exemplary system for identifying a plurality of logicalplanes formed of compute nodes of a subcommunicator in a parallelcomputer according to embodiments of the present invention. The systemof FIG. 1 includes a parallel computer (100), non-volatile memory forthe computer in the form of a data storage device (118), an outputdevice for the computer in the form of a printer (120), and aninput/output device for the computer in the form of a computer terminal(122).

The parallel computer (100) in the example of FIG. 1 includes aplurality of compute nodes (102). The compute nodes (102) are coupledfor data communications by several independent data communicationsnetworks including a high speed Ethernet network (174), a Joint TestAction Group (‘JTAG’) network (104), a global combining network (106)which is optimized for collective operations using a binary tree networktopology, and a point-to-point network (108), which is optimized forpoint-to-point operations using a torus network topology. The globalcombining network (106) is a data communications network that includesdata communications links connected to the compute nodes (102) so as toorganize the compute nodes (102) as a binary tree. Each datacommunications network is implemented with data communications linksamong the compute nodes (102). The data communications links providedata communications for parallel operations among the compute nodes(102) of the parallel computer (100).

The compute nodes (102) of the parallel computer (100) are organizedinto at least one operational group (132) of compute nodes forcollective parallel operations on the parallel computer (100). Eachoperational group (132) of compute nodes is the set of compute nodesupon which a collective parallel operation executes. Each compute nodein the operational group (132) is assigned a unique rank that identifiesthe particular compute node in the operational group (132). Collectiveoperations are implemented with data communications among the computenodes of an operational group. Collective operations are those functionsthat involve all the compute nodes of an operational group (132). Acollective operation is an operation, a message-passing computer programinstruction that is executed simultaneously, that is, at approximatelythe same time, by all the compute nodes in an operational group (132) ofcompute nodes. Such an operational group (132) may include all thecompute nodes (102) in a parallel computer (100) or a subset all thecompute nodes (102). Collective operations are often built aroundpoint-to-point operations. A collective operation requires that allprocesses on all compute nodes within an operational group (132) callthe same collective operation with matching arguments. A ‘broadcast’ isan example of a collective operation for moving data among compute nodesof an operational group. A ‘reduce’ operation is an example of acollective operation that executes arithmetic or logical functions ondata distributed among the compute nodes of an operational group (132).An operational group (132) may be implemented as, for example, an MPI‘communicator’ or a subset of the communicator, called asubcommunicator.

‘MPI’ refers to ‘Message Passing Interface,’ a prior art parallelcommunications library, a module of computer program instructions fordata communications on parallel computers. Examples of prior-artparallel communications libraries that may be improved for use insystems configured according to embodiments of the present inventioninclude MPI and the ‘Parallel Virtual Machine’ (‘PVM’) library. PVM wasdeveloped by the University of Tennessee, The Oak Ridge NationalLaboratory and Emory University. MPI is promulgated by the MPI Forum, anopen group with representatives from many organizations that define andmaintain the MPI standard. MPI at the time of this writing is a de factostandard for communication among compute nodes running a parallelprogram on a distributed memory parallel computer. This specificationsometimes uses MPI terminology for ease of explanation, although the useof MPI as such is not a requirement or limitation of the presentinvention.

Some collective operations have a single originating or receivingprocess running on a particular compute node in an operational group(132). For example, in a ‘broadcast’ collective operation, the processon the compute node that distributes the data to all the other computenodes is an originating process. In a ‘gather’ operation, for example,the process on the compute node that received all the data from theother compute nodes is a receiving process. The compute node on whichsuch an originating or receiving process runs is referred to as alogical root.

Most collective operations are variations or combinations of four basicoperations: broadcast, gather, scatter, and reduce. The interfaces forthese collective operations are defined in the MPI standards promulgatedby the MPI Forum. Algorithms for executing collective operations,however, are not defined in the MPI standards. In a broadcast operation,all processes specify the same root process, whose buffer contents willbe sent. Processes other than the root specify receive buffers. Afterthe operation, all buffers contain the message from the root process.

A scatter operation, like the broadcast operation, is also a one-to-manycollective operation. In a scatter operation, the logical root dividesdata on the root into segments and distributes a different segment toeach compute node in the operational group (132). In scatter operation,all processes typically specify the same receive count. The sendarguments are only significant to the root process, whose bufferactually contains sendcount*N elements of a given datatype, where N isthe number of processes in the given group of compute nodes. The sendbuffer is divided and dispersed to all processes (including the processon the logical root). Each compute node is assigned a sequentialidentifier termed a ‘rank.’ After the operation, the root has sentsendcount data elements to each process in increasing rank order. Rank 0receives the first sendcount data elements from the send buffer. Rank 1receives the second sendcount data elements from the send buffer, and soon.

A gather operation is a many-to-one collective operation that is acomplete reverse of the description of the scatter operation. That is, agather is a many-to-one collective operation in which elements of adatatype are gathered from the ranked compute nodes into a receivebuffer in a root node.

A reduction operation is also a many-to-one collective operation thatincludes an arithmetic or logical function performed on two dataelements. All processes specify the same ‘count’ and the same arithmeticor logical function. After the reduction, all processes have sent countdata elements from compute node send buffers to the root process. In areduction operation, data elements from corresponding send bufferlocations are combined pair-wise by arithmetic or logical operations toyield a single corresponding element in the root process' receivebuffer. Application specific reduction operations can be defined atruntime. Parallel communications libraries may support predefinedoperations. MPI, for example, provides the following pre-definedreduction operations:

MPI_MAX maximum MPI_MIN minimum MPI_SUM sum MPI_PROD product MPI_LANDlogical and MPI_BAND bitwise and MPI_LOR logical or MPI_BOR bitwise orMPI_LXOR logical exclusive or MPI_BXOR bitwise exclusive or

In addition to compute nodes, the parallel computer (100) includesinput/output (‘I/O’) nodes (110, 114) coupled to compute nodes (102)through the global combining network (106). The compute nodes (102) inthe parallel computer (100) may be partitioned into processing sets suchthat each compute node in a processing set is connected for datacommunications to the same I/O node. Each processing set, therefore, iscomposed of one I/O node and a subset of compute nodes (102). The ratiobetween the number of compute nodes to the number of I/O nodes in theentire system typically depends on the hardware configuration for theparallel computer (102). For example, in some configurations, eachprocessing set may be composed of eight compute nodes and one I/O node.In some other configurations, each processing set may be composed ofsixty-four compute nodes and one I/O node. Such example are forexplanation only, however, and not for limitation. Each I/O nodeprovides I/O services between compute nodes (102) of its processing setand a set of I/O devices. In the example of FIG. 1, the I/O nodes (110,114) are connected for data communications I/O devices (118, 120, 122)through local area network (‘LAN’) (130) implemented using high-speedEthernet.

The parallel computer (100) of FIG. 1 also includes a service node (116)coupled to the compute nodes through one of the networks (104). Servicenode (116) provides services common to pluralities of compute nodes,administering the configuration of compute nodes, loading programs intothe compute nodes, starting program execution on the compute nodes,retrieving results of program operations on the compute nodes, and soon. Service node (116) runs a service application (124) and communicateswith users (128) through a service application interface (126) that runson computer terminal (122).

The parallel computer (100) of FIG. 1 operates generally for identifyinga plurality of logical planes formed of compute nodes of asubcommunicator in a parallel computer in accordance with embodiments ofthe present invention. A communicator is an example of an operationalgroup, a set of compute nodes configured for data communications andcollective operations. A subcommunicator is a subset of thecommunicator. A communicator is generally established in a regular datacommunications topology—a mesh, grid, or torus for example. A regulartopology is one in which no gaps (disconnects in communication paths)exist between nodes. Generally, a regular topology is axial, meaningthat the topology is defined among one or more axes, such as an X axis,Y axis, and Z axis. An example of a communicator having a regulartopology is depicted in FIG. 7. In that example, the communicatorincludes 30 nodes in a regular, axial grid pattern.

An irregular topology is a topology in which gaps exist between nodes inthe same axis. Consider as an example, the communicator in FIG. 7. Thenodes in the communicator of FIG. 7 that are coupled by links representnodes of a subcommunicator. As can be seen in FIG. 7, thesubcommunicator is an irregular topology. Node 0 for example, isseparated from node 2, both of which are in the same axis and part ofthe same subcommunicator.

Some data communications optimizations often rely on an underlyingregular topology—axial or planar topology—to be performed. A deposit bitoptimization, for example, generally enables fast communication alongone or more axes of a set of compute nodes. The deposit bit optimizationenables a communications adapter of a first node to receive a messageand forward the message to the next node in the same axis immediately aswell as the next node in a next (or orthogonal) axis, even beforecopying the message to local memory for a process executing on the firstcompute node. The communication adapter of each compute node receivingthat message, can carry out exactly the same steps such that a singlemessage may be broadcast down a one or more axes very quickly. When thecompute nodes on one or more axes, however, include one or more datacommunication gaps, the bit deposit optimization fails.

To that end, parallel computer (100) of FIG. 1 operates generally foridentifying a plurality of logical planes formed of compute nodes of asubcommunicator in a parallel computer in accordance with embodiments ofthe present invention. The term ‘logical’ here refers to a topology thatis not a physical topology. Identifying a plurality of logical planesformed of compute nodes of a subcommunicator may be carried out by eachnode of the subcommunicator, in parallel. That is, each compute node ofthe subcommunicator may separately, and in parallel, identify logicalplanes for which that compute node is a part. Each compute node(referred to as a ‘plane building node’ here when identifying logicalplanes for which the compute node is included) may, for a plurality ofdimensions beginning with a first dimension: establish in a positivedirection of the first dimension, all logical planes that include theplane building node and compute nodes of the subcommunicator in apositive direction of a second dimension, where the second dimension isorthogonal to the first dimension. Then the plane building node mayestablish in a negative direction of the first dimension, all logicalplanes that include the plane building node and compute nodes of thesubcommunicator in the positive direction of the second dimension. Eachstep described here may be carried out in an iterative fashion: forexample, identifying a first plane in the positive direction of thefirst dimension, identifying a second plane in the positive direction ofthe first dimension, and so on, until all planes including the computenode in the positive direction of the first dimension have beenidentified. Such an iterative process is described below in detail withrespect to FIGS. 7-11B.

As mentioned above, identifying a plurality of logical planes formed ofcompute nodes of a subcommunicator in a parallel computer according toembodiments of the present invention is generally implemented on aparallel computer that includes a plurality of compute nodes organizedfor collective operations through at least one data communicationsnetwork. In fact, such parallel computers may include thousands of suchcompute nodes. Each compute node is in turn itself a kind of computerwhich may be composed of one or more computer processing cores, its owncomputer memory, and its own input/output adapters. For furtherexplanation, therefore, FIG. 2 sets forth a block diagram of an examplecompute node (102) useful in a parallel computer capable of identifyinga plurality of logical planes formed of compute nodes of asubcommunicator in a parallel computer according to embodiments of thepresent invention. The compute node (102) of FIG. 2 includes a pluralityof processing cores (165) as well as RAM (156). The processing cores(165) of FIG. 2 may be configured on one or more integrated circuitdies. Processing cores (165) are connected to RAM (156) through ahigh-speed memory bus (155) and through a bus adapter (194) and anextension bus (168) to other components of the compute node. Stored inRAM (156) is an application program (226), a module of computer programinstructions that carries out parallel, user-level data processing usingparallel algorithms.

Also stored RAM (156) is a parallel communications library (161), alibrary of computer program instructions that carry out parallelcommunications among compute nodes, including point-to-point operationsas well as collective operations. A library of parallel communicationsroutines may be developed from scratch for use in systems according toembodiments of the present invention, using a traditional programminglanguage such as the C programming language, and using traditionalprogramming methods to write parallel communications routines that sendand receive data among nodes on two independent data communicationsnetworks. Alternatively, existing prior art libraries may be improved tooperate according to embodiments of the present invention. Examples ofprior-art parallel communications libraries include the ‘Message PassingInterface’ (‘MPI’) library and the ‘Parallel Virtual Machine’ (‘PVM’)library.

The compute node (102) of FIG. 2 operates generally for identifying aplurality of logical planes formed of compute nodes of a subcommunicatorin a parallel computer in accordance with embodiments of the presentinvention. The communicator, of which the subcommunicator is a part, maybe a regular topology such as a grid or a mesh. The parallelcommunications library (161) may be configured to identify such logicalplanes, by carrying out the following steps iteratively for each of aplurality of dimensions beginning with a first dimension: establishing,by a plane building node (the compute node 102 in the example of FIG.2), in a positive direction of the first dimension, all logical planesthat include the plane building node and compute nodes of thesubcommunicator in a positive direction of a second dimension. In thisexample, the second dimension is orthogonal to the first dimension—the Xdimension, for example may be the first dimension, and the Y dimensionmay be the second dimension. Then, the plane building node (102) mayestablish, in a negative direction of the first dimension, all logicalplanes that include the plane building node and compute nodes of thesubcommunicator in the positive direction of the second dimension. Thelogical planes established by the plane building node (1020 may bestored in a list of logical planes (230).

Because all compute nodes of the subcommunicator separately and inparallel identify the logical planes of the subcommunicator of which thecompute node is included, some compute nodes may identify, separately,identical logical planes. To filter the duplicate planes identified bythe compute nodes of the subcommunicator, at least one compute node inthe subcommunicator may construct a set (232) of unique logical planesof the subcommunicator in dependence upon the logical planes establishedby each node. Constructing such a set (232) of unique logical planes ofthe subcommunicator may be carried out in various ways. In one way, thecompute node may establish an list, add an entry in the list for alogical plane identified by a compute node, and before adding anotherentry for another logical plane determining that the logical plane to beadded is not already included in the list. In this way, only uniqueentries are added to the last. Each entry, for example, may be a vectorof four coordinates: coordinates of a compute node at the lower left ofthe plane, coordinates of the compute node at the lower right of theplane, coordinates of the compute node of at the upper left of theplane, and coordinates of the compute node at the upper right of theplane. Once the list is complete (all logical planes established by thecompute nodes of the subcommunicator have been processed and only uniqueplanes have been included in the list), the list may be broadcast to allcompute nodes of the subcommunicator. Then, any subcommunicator node mayrefer to the list of unique planes to transmit messages among thesubcommunicator using optimizations that rely on planar topologies.

Also stored in RAM (156) is an operating system (162), a module ofcomputer program instructions and routines for an application program'saccess to other resources of the compute node. It is typical for anapplication program and parallel communications library in a computenode of a parallel computer to run a single thread of execution with nouser login and no security issues because the thread is entitled tocomplete access to all resources of the node. The quantity andcomplexity of tasks to be performed by an operating system on a computenode in a parallel computer therefore are smaller and less complex thanthose of an operating system on a serial computer with many threadsrunning simultaneously. In addition, there is no video I/O on thecompute node (102) of FIG. 2, another factor that decreases the demandson the operating system. The operating system (162) may therefore bequite lightweight by comparison with operating systems of generalpurpose computers, a pared down version as it were, or an operatingsystem developed specifically for operations on a particular parallelcomputer. Operating systems that may usefully be improved, simplified,for use in a compute node include UNIX™, Linux™, Windows XP™, AIX™,IBM's i5/OS™, and others as will occur to those of skill in the art.

The example compute node (102) of FIG. 2 includes several communicationsadapters (172, 176, 180, 188) for implementing data communications withother nodes of a parallel computer. Such data communications may becarried out serially through RS-232 connections, through external busessuch as USB, through data communications networks such as IP networks,and in other ways as will occur to those of skill in the art.Communications adapters implement the hardware level of datacommunications through which one computer sends data communications toanother computer, directly or through a network. Examples ofcommunications adapters useful in apparatus useful for constructing alogical, regular axis topology from an irregular topology of asubcommunicator's compute nodes in a parallel computer include modemsfor wired communications, Ethernet (IEEE 802.3) adapters for wirednetwork communications, and 802.11b adapters for wireless networkcommunications.

The data communications adapters in the example of FIG. 2 include aGigabit Ethernet adapter (172) that couples example compute node (102)for data communications to a Gigabit Ethernet (174). Gigabit Ethernet isa network transmission standard, defined in the IEEE 802.3 standard,that provides a data rate of 1 billion bits per second (one gigabit).Gigabit Ethernet is a variant of Ethernet that operates over multimodefiber optic cable, single mode fiber optic cable, or unshielded twistedpair.

The data communications adapters in the example of FIG. 2 include a JTAGSlave circuit (176) that couples example compute node (102) for datacommunications to a JTAG Master circuit (178). JTAG is the usual nameused for the IEEE 1149.1 standard entitled Standard Test Access Port andBoundary-Scan Architecture for test access ports used for testingprinted circuit boards using boundary scan. JTAG is so widely adaptedthat, at this time, boundary scan is more or less synonymous with JTAG.JTAG is used not only for printed circuit boards, but also forconducting boundary scans of integrated circuits, and is also useful asa mechanism for debugging embedded systems, providing a convenientalternative access point into the system. The example compute node ofFIG. 2 may be all three of these: It typically includes one or moreintegrated circuits installed on a printed circuit board and may beimplemented as an embedded system having its own processing core, itsown memory, and its own I/O capability. JTAG boundary scans through JTAGSlave (176) may efficiently configure processing core registers andmemory in compute node (102) for use in dynamically reassigning aconnected node to a block of compute nodes useful in systems forconstructing a logical, regular axis topology from an irregular topologyof a subcommunicator's compute nodes in a parallel computer toembodiments of the present invention.

The data communications adapters in the example of FIG. 2 include aPoint-To-Point Network Adapter (180) that couples example compute node(102) for data communications to a network (108) that is optimal forpoint-to-point message passing operations such as, for example, anetwork configured as a three-dimensional torus or mesh. ThePoint-To-Point Adapter (180) provides data communications in sixdirections on three communications axes, x, y, and z, through sixbidirectional links: +x (181), −x (182), +y (183), −y (184), +z (185),and −z (186).

The data communications adapters in the example of FIG. 2 include aGlobal Combining Network Adapter (188) that couples example compute node(102) for data communications to a global combining network (106) thatis optimal for collective message passing operations such as, forexample, a network configured as a binary tree. The Global CombiningNetwork Adapter (188) provides data communications through threebidirectional links for each global combining network (106) that theGlobal Combining Network Adapter (188) supports. In the example of FIG.2, the Global Combining Network Adapter (188) provides datacommunications through three bidirectional links for global combiningnetwork (106): two to children nodes (190) and one to a parent node(192).

The example compute node (102) includes multiple arithmetic logic units(‘ALUs’). Each processing core (165) includes an ALU (166), and aseparate ALU (170) is dedicated to the exclusive use of the GlobalCombining Network Adapter (188) for use in performing the arithmetic andlogical functions of reduction operations, including an allreduceoperation. Computer program instructions of a reduction routine in aparallel communications library (161) may latch an instruction for anarithmetic or logical function into an instruction register (169). Whenthe arithmetic or logical function of a reduction operation is a ‘sum’or a ‘logical OR,’ for example, the collective operations adapter (188)may execute the arithmetic or logical operation by use of the ALU (166)in the processing core (165) or, typically much faster, by use of thededicated ALU (170) using data provided by the nodes (190, 192) on theglobal combining network (106) and data provided by processing cores(165) on the compute node (102).

Often when performing arithmetic operations in the global combiningnetwork adapter (188), however, the global combining network adapter(188) only serves to combine data received from the children nodes (190)and pass the result up the network (106) to the parent node (192).Similarly, the global combining network adapter (188) may only serve totransmit data received from the parent node (192) and pass the data downthe network (106) to the children nodes (190). That is, none of theprocessing cores (165) on the compute node (102) contribute data thatalters the output of ALU (170), which is then passed up or down theglobal combining network (106). Because the ALU (170) typically does notoutput any data onto the network (106) until the ALU (170) receivesinput from one of the processing cores (165), a processing core (165)may inject the identity element into the dedicated ALU (170) for theparticular arithmetic operation being perform in the ALU (170) in orderto prevent alteration of the output of the ALU (170). Injecting theidentity element into the ALU, however, often consumes numerousprocessing cycles. To further enhance performance in such cases, theexample compute node (102) includes dedicated hardware (171) forinjecting identity elements into the ALU (170) to reduce the amount ofprocessing core resources required to prevent alteration of the ALUoutput. The dedicated hardware (171) injects an identity element thatcorresponds to the particular arithmetic operation performed by the ALU.For example, when the global combining network adapter (188) performs abitwise OR on the data received from the children nodes (190), dedicatedhardware (171) may inject zeros into the ALU (170) to improveperformance throughout the global combining network (106).

For further explanation, FIG. 3A sets forth a block diagram of anexample Point-To-Point Adapter (180) useful in systems for identifying aplurality of logical planes formed of compute nodes of a subcommunicatorin a parallel computer according to embodiments of the presentinvention. The Point-To-Point Adapter (180) is designed for use in adata communications network optimized for point-to-point operations, anetwork that organizes compute nodes in a three-dimensional torus ormesh. The Point-To-Point Adapter (180) in the example of FIG. 3Aprovides data communication along an x-axis through four unidirectionaldata communications links, to and from the next node in the −x direction(182) and to and from the next node in the +x direction (181). ThePoint-To-Point Adapter (180) of FIG. 3A also provides data communicationalong a y-axis through four unidirectional data communications links, toand from the next node in the −y direction (184) and to and from thenext node in the +y direction (183). The Point-To-Point Adapter (180) ofFIG. 3A also provides data communication along a z-axis through fourunidirectional data communications links, to and from the next node inthe −z direction (186) and to and from the next node in the +z direction(185).

For further explanation, FIG. 3B sets forth a block diagram of anexample Global Combining Network Adapter (188) useful in systems foridentifying a plurality of logical planes formed of compute nodes of asubcommunicator in a parallel computer according to embodiments of thepresent invention. The Global Combining Network Adapter (188) isdesigned for use in a network optimized for collective operations, anetwork that organizes compute nodes of a parallel computer in a binarytree. The Global Combining Network Adapter (188) in the example of FIG.3B provides data communication to and from children nodes of a globalcombining network through four unidirectional data communications links(190), and also provides data communication to and from a parent node ofthe global combining network through two unidirectional datacommunications links (192).

For further explanation, FIG. 4 sets forth a line drawing illustratingan example data communications network (108) optimized forpoint-to-point operations useful in systems capable of identifying aplurality of logical planes formed of compute nodes of a subcommunicatorin a parallel computer according to embodiments of the presentinvention. In the example of FIG. 4, dots represent compute nodes (102)of a parallel computer, and the dotted lines between the dots representdata communications links (103) between compute nodes. The datacommunications links are implemented with point-to-point datacommunications adapters similar to the one illustrated for example inFIG. 3A, with data communications links on three axis, x, y, and z, andto and fro in six directions +x (181), −x (182), +y (183), −y (184), +z(185), and −z (186). The links and compute nodes are organized by thisdata communications network optimized for point-to-point operations intoa three dimensional mesh (105). The mesh (105) has wrap-around links oneach axis that connect the outermost compute nodes in the mesh (105) onopposite sides of the mesh (105). These wrap-around links form a torus(107). Each compute node in the torus has a location in the torus thatis uniquely specified by a set of x, y, z coordinates. Readers will notethat the wrap-around links in the y and z directions have been omittedfor clarity, but are configured in a similar manner to the wrap-aroundlink illustrated in the x direction. For clarity of explanation, thedata communications network of FIG. 4 is illustrated with only 27compute nodes, but readers will recognize that a data communicationsnetwork optimized for point-to-point operations for use in identifying aplurality of logical planes formed of compute nodes of a subcommunicatorin a parallel computer according to embodiments of the present inventionin accordance with embodiments of the present invention may contain onlya few compute nodes or may contain thousands of compute nodes. For easeof explanation, the data communications network of FIG. 4 is illustratedwith only three dimensions, but readers will recognize that a datacommunications network optimized for point-to-point operations for usein constructing a logical, regular axis topology from an irregulartopology of a subcommunicator's compute nodes in a parallel computer inaccordance with embodiments of the present invention may in facet beimplemented in two dimensions, four dimensions, five dimensions, and soon. Several supercomputers now use five dimensional mesh or torusnetworks, including, for example, IBM's Blue Gene Q™.

For further explanation, FIG. 5 sets forth a line drawing illustratingan example global combining network (106) useful in systems capable ofconstructing a logical, regular axis topology from an irregular topologyof a subcommunicator's compute nodes in a parallel computer according toembodiments of the present invention. The example data communicationsnetwork of FIG. 5 includes data communications links (103) connected tothe compute nodes so as to organize the compute nodes as a tree. In theexample of FIG. 5, dots represent compute nodes (102) of a parallelcomputer, and the dotted lines (103) between the dots represent datacommunications links between compute nodes. The data communicationslinks are implemented with global combining network adapters similar tothe one illustrated for example in FIG. 3B, with each node typicallyproviding data communications to and from two children nodes and datacommunications to and from a parent node, with some exceptions. Nodes inthe global combining network (106) may be characterized as a physicalroot node (202), branch nodes (204), and leaf nodes (206). The physicalroot (202) has two children but no parent and is so called because thephysical root node (202) is the node physically configured at the top ofthe binary tree. The leaf nodes (206) each has a parent, but leaf nodeshave no children. The branch nodes (204) each has both a parent and twochildren. The links and compute nodes are thereby organized by this datacommunications network optimized for collective operations into a binarytree (106). For clarity of explanation, the data communications networkof FIG. 5 is illustrated with only 31 compute nodes, but readers willrecognize that a global combining network (106) optimized for collectiveoperations for use in constructing a logical, regular axis topology froman irregular topology of a subcommunicator's compute nodes in a parallelcomputer in accordance with embodiments of the present invention maycontain only a few compute nodes or may contain thousands of computenodes.

In the example of FIG. 5, each node in the tree is assigned a unitidentifier referred to as a ‘rank’ (250). The rank actually identifies atask or process that is executing a parallel operation according toembodiments of the present invention. Using the rank to identify a nodeassumes that only one such task is executing on each node. To the extentthat more than one participating task executes on a single node, therank identifies the task as such rather than the node. A rank uniquelyidentifies a task's location in the tree network for use in bothpoint-to-point and collective operations in the tree network. The ranksin this example are assigned as integers beginning with 0 assigned tothe root tasks or root node (202), 1 assigned to the first node in thesecond layer of the tree, 2 assigned to the second node in the secondlayer of the tree, 3 assigned to the first node in the third layer ofthe tree, 4 assigned to the second node in the third layer of the tree,and so on. For ease of illustration, only the ranks of the first threelayers of the tree are shown here, but all compute nodes in the treenetwork are assigned a unique rank.

For further explanation, FIG. 6 sets forth a flow chart illustrating anexample method for identifying a plurality of logical planes formed ofcompute nodes of a subcommunicator in a parallel computer according toembodiments of the present invention. The method of FIG. 6 is carriedout in a parallel computer in which the subcommunicator includes asubset of a communicator's compute nodes and the communicator's computenodes are organized into a regular topology that includes a plurality ofaxial dimensions. In some embodiments the regular topology is a torusnetwork topology that includes N-dimensions, where N is an integergreater than one—a five dimensional torus network topology for example.

The method of FIG. 6 includes several steps that are carried outseparately and in parallel by each compute node (610) of thesubcommunicator. Those steps are also carried out iteratively, for aplurality of dimensions beginning with a first dimension. One of thosesteps includes establishing (602), by a plane building node, in apositive direction of the first dimension, all logical planes thatinclude the plane building node and compute nodes of the subcommunicatorin a positive direction of a second dimension. In some embodiments ofthe present invention, the second dimension is orthogonal to the firstdimension. Establishing (602), in a positive direction of the firstdimension, all logical planes that include the plane building node andcompute nodes of the subcommunicator in a positive direction of a seconddimension may include assigning the plane building node to be the lowerleft node of a logical plane of the subcommunicator. After assigning theplane building node as the lower left node, the following steps may becarried out iteratively, beginning with a node one hop away from thelower left node in a positive direction of the first dimension until anode at a next hop away from the lower left node is not included in thesubcommunicator. First, the plane building node may assign a node at anext hop away from the lower left node in the positive direction of thefirst dimension to be the lower right node of the logical plane of thesubcommunicator. Next, the plane building node, may iteratively,beginning with nodes one hop away from the lower left node and lowerright node in a positive direction of a second dimension until a node ata next hop away from the lower left or lower right node is not includedin the subcommunicator: assign a node at a next hop away from the lowerleft node in the positive direction of the second dimension to be theupper left node of the logical plane and assigning a node at a next hopaway from the lower right node in the positive direction of the seconddimension to be the upper right node of the logical plane. The stepsdescribed here include nested iterative loops. The outer iterative loopadds a node in the same, first dimension as the plane building node aspart of the plane. Then, within the outer iterative loop, the planebuilding node iteratively adds nodes in the second dimension to formplanes.

For purposes of explanation FIGS. 8A, 8B, 9A, and 9B, set forthiterations of the nested iterative loops described above. In FIG. 8A,the compute node 7 (the plane building node for this example), assignsitself to be the lower left node of a logical plane of thesubcommunicator. Then, the plane building node assigns a node at a nexthop away (node 8) from the lower left node in the positive direction ofthe first dimension (the X-dimension) to be the lower right node of thelogical plane of the subcommunicator. Note, as mentioned above, thatthis is step is carried out only if the node at a next hop away is alsoincluded in the subcommunicator. That is, if node 8 were not included inthe subcommunicator, no planes in the positive direction of theX-dimension could be formed that include node 7. Next, node 7 assigns anode at a next hop away (node 13) from the lower left node in thepositive direction of the second dimension (the Y-dimension) to be theupper left node of the logical plane. Again, this step is carried outonly if the node is also in the same subcommunicator. Then, node 7assigns a node at a next hop away from the lower right node (node 14) inthe positive direction of the second dimension to be the upper rightnode of the logical plane. Again, this step is carried out only if thenode is also in the same subcommunicator. At this point, node 7 hasidentified a plane that includes node 7, node 8, node 13, and node 14.

While maintaining node 7 as the lower left node and node 8 as the lowerright node, node 7 then proceeds, in FIG. 8B, with a second iteration ofestablishing a plane in the positive direction of the second dimensionby adding nodes of the same subcommunicator an additional hop away fromthe previous upper left and upper right nodes to the subcommunicator. Inthe example of FIG. 8B, nodes 19 and 20 are included in thesubcommunicator and as such are set as the upper left and upper rightnodes of a second logical plane of which node 7 is a part. At thispoint, node 7 has established two logical planes: the one described inFIG. 8A and the plane formed of nodes 7, 8, 19, and 20 in FIG. 8B.

Because neither node 25 nor 26 (nodes an additional hop away from thepreviously assigned upper left and right nodes) are not part of thesubcommunicator, node 7 ceases iteratively adding nodes in the positivedirection of the Y dimension to logical planes. Instead, a seconditeration of the outer iterative loop begins as depicted in FIG. 9A. InFIG. 9A, node 7 assigns a node that is included in the subcommunicatorand is also an additional hop away from the previous lower right node inthe positive direction of the X-dimension to be the lower right node. Inthe example of FIG. 9A, node 9 is assigned as the lower right node.Then, in a manner similar to the example of FIG. 8A, node 7 assigns node13 (the node a next hop away from node 7 in the Y-dimension) to be theupper left node and assigns node 15 (the node a next hop away from thelower right node in the Y-dimension) to be the upper right node.

FIG. 9B, depicts the second iteration in the Y dimension. In thisexample, node 7 assigns node 19 (the node a next hop away from theprevious upper left node) to be the upper left node and node 21 (thenode a next hop away from the previous upper right node) to be the upperright node.

As can be seen from FIGS. 8A-9B, the plane building node effectivelyestablishes logical planes beginning one hop away in the positive Xdimension, then iteratively one hop away in the positive Y dimension.Then the plane building node begins again another hop away in thepositive X dimensions, followed by iterations one hop away in thepositive Y dimension. Any iteration that encounters a node one hop awaythat is not included in the subcommunicator, causes the establishment ofplanes to cease. In some embodiments, the plane building node alsoestablishes planes in the negative direction of the second dimension ina manner similar to that described above. That is, after establishingplanes in the positive direction of the first dimension and the positivedirection of the second dimension, the plane building node may establishin the positive direction of the first dimension, all logical planesthat include the plane building node and compute nodes of thesubcommunicator in a negative direction of the second dimension.Further, after establishing planes in the negative direction of thefirst dimension and positive direction of the second dimension, theplane building node may also establish in the negative direction of thefirst dimension, all logical planes that include the plane building nodeand compute nodes of the subcommunicator in the negative direction ofthe second dimension. In this way, each node may identify in eachdirection of each plane, all logical planes of which the node is a part.

Returning now to FIG. 6: the method of FIG. 6 also includes establishing(604), by the plane building node, in a negative direction of the firstdimension, all logical planes that include the plane building node andcompute nodes of the subcommunicator in the positive direction of thesecond dimension. Establishing (604) in a negative direction of thefirst dimension, all logical planes that include the plane building nodeand compute nodes of the subcommunicator in the positive direction ofthe second dimension may be carried out in various ways, including in amanner similar to that described above for the positive direction of thefirst dimension. The plane building node may assign itself to be thelower right node of a logical plane of the subcommunicator anditeratively, beginning with a node one hop away from the lower rightnode in the negative direction of the first dimension until a node at anext hop away from the lower right node is not included in thesubcommunicator: assign a node at a next hop away from the lower rightnode in the negative direction of the first dimension to be the lowerleft node of the logical plane of the subcommunicator. Further, as partof that iteration, the plane building node may carry out a seconditerative loop beginning with a node one hop away from the lower rightnode and a node one hop away from the lower left node in the positivedirection of the second dimension until a node at a next hop away fromthe lower right or lower left node is not included in thesubcommunicator. Such iterations may include assigning a node at a nexthop away from the lower right node in the positive direction of thesecond dimension to be the upper right node of the logical plane andassigning a node at a next hop away from the lower left node in thepositive direction of the second dimension to be the upper left node ofthe logical plane.

For further explanation, consider the example provided in FIGS. 10A and10B. In FIG. 10A, the plane building node (node 7) assigns itself to bethe lower right node. Then, the plane building node sets a node one hopaway in the negative direction of the X-dimension to be the lower leftnode only if that node is included in the subcommunicator. If that nodeis not included in the subcommunicator no planes can be built in thenegative direction of the X-dimension that include node 7. In thisexample, however, node 6 is included in the subcommunicator and isassigned to be the lower left node. Then, node 7 assigns node 12 (a nodeone hop away from the lower left node) to be the upper left node andassigns node 13 (a node one hop away from the lower right node) to bethe upper right node of a plane. Thus, a first plane is established. Itis noted, again, that if either of node 12 or node 13 were not includedin the subcommunicator, a plane could not be established and node 7would cease attempting to establish logical planes in the negativedirection of the X-dimension.

In FIG. 10B, node 7 proceeds with a second iteration in the positivedirection of the Y-dimension while maintaining the lower left node atnode 6. In this example, node 7 assigns node 18 (a node one hop awayfrom the previous upper left node) to be the upper left node and assignsnode 19 (a node one hop away from the previous upper right node) to bethe upper right node. Thus, a second plane is established. At thispoint, there is no node in the subcommunicator included one hop awayfrom the node 18 and node 19 and, as such, node 7 ceases attempting toestablish logical planes in the positive direction of the Y-dimension.

Readers of skill in the art will recognize that two dimensions areutilized in FIGS. 7-10B as means for explanation only, not limitation.The steps set forth above may be applied for each of any number ofdimensions. Further, these steps may be extended for higher-dimensionalshapes than planes. Consider, for example, that while a plane is definedby four nodes, a cube may be defined by eight.

The following pseudocode is yet another example of the steps 602 and 604of the method of FIG. 6:

//ll=lower left, lr=lower right, ul=upper right, ur=upper right // givenN dimensions 0 <= m < N //coordinate of each node is expressed asnode.coords[array of size (N)] // each plane building node separatelyand in parallel may execute the following: for m = 0 to N−1 {  BuildPositivePlane(PBN, m);   BuildNegativePlane(PBN, m);   }BuildPositivePlane (node_ll, m) {   let node_lr = node_ll; //initializeeach node's coordinates to be   the plane building   let node_ul =node_ll; // node's coordinates   let node_ur = node_ll;   for (d = 1; d< length_of(m); d++)   {    node_lr.coords[m] = node_ll.coords[m] + d;   node_ur.coords[m] = node_ll.coords[m] + d;      if (node_lr is insubcommunicator)       {       for (i = 0; i <length_of(next_dimension); i++)         {         node_ul.coords[next_dimension] += i;         node_ur.coords[next_dimension] += i;          if (node_ul &&node_ur are in the linear          communicator)            create aplane spanning nodes (ll, lr, ul, ur);         }       }      elsebreak;   } } BuildNegativePlane (node_lr, m) {   let node_ll = node_lr;// initialize each node's coordinates   to be the plane building   letnode_ul = node_lr; // node's coordinates   let node_ur = node_lr;   for(d = 1; d < length_of(m); d++)   {    node_ll.coords[m] =node_lr.coords[m] − d    node_ur.coords[m] = node_lr.coords[m] − d     if (node_ll is in linear communicator)       {       for (i = 0; i< length_of(next_dimension); i++)         {         node_ul.coords[next_dimension] += i;         node_ur.coords[next_dimension] += i;          if (node_ul &&node_ur are in the linear          communicator)            create aplane spanning nodes (ll, lr, ul, ur)         }       }    else break;  } }

Returning now to the method of FIG. 6, the method also includesconstructing (606) a set of unique logical planes of the subcommunicatorin dependence upon the logical planes established by each node andperforming (608) data communications amongst the compute nodes of thesubcommunicator utilizing optimization techniques based on the topologyof the unique logical planes

As will be appreciated by one skilled in the art, aspects of the presentinvention may be embodied as a system, method or computer programproduct. Accordingly, aspects of the present invention may take the formof an entirely hardware embodiment, an entirely software embodiment(including firmware, resident software, micro-code, etc.) or anembodiment combining software and hardware aspects that may allgenerally be referred to herein as a “circuit,” “module” or “system.”Furthermore, aspects of the present invention may take the form of acomputer program product embodied in one or more computer readablemedium(s) having computer readable program code embodied thereon.

Any combination of one or more computer readable medium(s) may beutilized. The computer readable medium may be a computer readabletransmission medium or a computer readable storage medium. A computerreadable storage medium may be, for example, but not limited to, anelectronic, magnetic, optical, electromagnetic, infrared, orsemiconductor system, apparatus, or device, or any suitable combinationof the foregoing. More specific examples (a non-exhaustive list) of thecomputer readable storage medium would include the following: anelectrical connection having one or more wires, a portable computerdiskette, a hard disk, a random access memory (RAM), a read-only memory(ROM), an erasable programmable read-only memory (EPROM or Flashmemory), an optical fiber, a portable compact disc read-only memory(CD-ROM), an optical storage device, a magnetic storage device, or anysuitable combination of the foregoing. In the context of this document,a computer readable storage medium may be any tangible medium that cancontain, or store a program for use by or in connection with aninstruction execution system, apparatus, or device.

A computer readable transmission medium may include a propagated datasignal with computer readable program code embodied therein, forexample, in baseband or as part of a carrier wave. Such a propagatedsignal may take any of a variety of forms, including, but not limitedto, electro-magnetic, optical, or any suitable combination thereof. Acomputer readable transmission medium may be any computer readablemedium that is not a computer readable storage medium and that cancommunicate, propagate, or transport a program for use by or inconnection with an instruction execution system, apparatus, or device.

Program code embodied on a computer readable medium may be transmittedusing any appropriate medium, including but not limited to wireless,wireline, optical fiber cable, RF, etc., or any suitable combination ofthe foregoing.

Computer program code for carrying out operations for aspects of thepresent invention may be written in any combination of one or moreprogramming languages, including an object oriented programming languagesuch as Java, Smalltalk, C++ or the like and conventional proceduralprogramming languages, such as the “C” programming language or similarprogramming languages. The program code may execute entirely on theuser's computer, partly on the user's computer, as a stand-alonesoftware package, partly on the user's computer and partly on a remotecomputer or entirely on the remote computer or server. In the latterscenario, the remote computer may be connected to the user's computerthrough any type of network, including a local area network (LAN) or awide area network (WAN), or the connection may be made to an externalcomputer (for example, through the Internet using an Internet ServiceProvider).

Aspects of the present invention are described above with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems) and computer program products according to embodiments of theinvention. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer program instructions. These computer program instructions maybe provided to a processor of a general purpose computer, specialpurpose computer, or other programmable data processing apparatus toproduce a machine, such that the instructions, which execute via theprocessor of the computer or other programmable data processingapparatus, create means for implementing the functions/acts specified inthe flowchart and/or block diagram block or blocks.

These computer program instructions may also be stored in a computerreadable medium that can direct a computer, other programmable dataprocessing apparatus, or other devices to function in a particularmanner, such that the instructions stored in the computer readablemedium produce an article of manufacture including instructions whichimplement the function/act specified in the flowchart and/or blockdiagram block or blocks.

The computer program instructions may also be loaded onto a computer,other programmable data processing apparatus, or other devices to causea series of operational steps to be performed on the computer, otherprogrammable apparatus or other devices to produce a computerimplemented process such that the instructions which execute on thecomputer or other programmable apparatus provide processes forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowchart or block diagrams may represent a module, segment, or portionof code, which comprises one or more executable instructions forimplementing the specified logical function(s). It should also be notedthat, in some alternative implementations, the functions noted in theblock may occur out of the order noted in the figures. For example, twoblocks shown in succession may, in fact, be executed substantiallyconcurrently, or the blocks may sometimes be executed in the reverseorder, depending upon the functionality involved. It will also be notedthat each block of the block diagrams and/or flowchart illustration, andcombinations of blocks in the block diagrams and/or flowchartillustration, can be implemented by special purpose hardware-basedsystems that perform the specified functions or acts, or combinations ofspecial purpose hardware and computer instructions.

It will be understood from the foregoing description that modificationsand changes may be made in various embodiments of the present inventionwithout departing from its true spirit. The descriptions in thisspecification are for purposes of illustration only and are not to beconstrued in a limiting sense. The scope of the present invention islimited only by the language of the following claims.

1-8. (canceled)
 9. An apparatus for identifying a plurality of logicalplanes formed of compute nodes of a subcommunicator in a parallelcomputer, the apparatus comprising a computer processor, a computermemory operatively coupled to the computer processor, the computermemory having disposed within it computer program instructions that,when executed, cause the apparatus to carry out the steps of: for eachcompute node of the subcommunicator and iteratively, for a plurality ofdimensions beginning with a first dimension: establishing, by a planebuilding node, in a positive direction of the first dimension, alllogical planes that include the plane building node and compute nodes ofthe subcommunicator in a positive direction of a second dimension,wherein the second dimension is orthogonal to the first dimension; andestablishing, by the plane building node, in a negative direction of thefirst dimension, all logical planes that include the plane building nodeand compute nodes of the subcommunicator in the positive direction ofthe second dimension.
 10. The apparatus of claim 9, whereinestablishing, in a positive direction of the first dimension, alllogical planes that include the plane building node and compute nodes ofthe subcommunicator in a positive direction of a second dimension,further comprises: assigning the plane building node to be the lowerleft node of a logical plane of the subcommunicator; iteratively,beginning with a node one hop away from the lower left node in apositive direction of the first dimension until a node at a next hopaway from the lower left node is not included in the subcommunicator:assigning a node at a next hop away from the lower left node in thepositive direction of the first dimension to be the lower right node ofthe logical plane of the subcommunicator; and iteratively, beginningwith nodes one hop away from the lower left node and lower right node ina positive direction of a second dimension until a node at a next hopaway from the lower left or lower right node is not included in thesubcommunicator: assigning a node at a next hop away from the lower leftnode in the positive direction of the second dimension to be the upperleft node of the logical plane and assigning a node at a next hop awayfrom the lower right node in the positive direction of the seconddimension to be the upper right node of the logical plane.
 11. Theapparatus of claim 9, wherein establishing, by the plane building node,in a negative direction of the first dimension, all logical planes thatinclude the plane building node and compute nodes of the subcommunicatorin the positive direction of the second dimension, further comprises:assigning the plane building node to be the lower right node of alogical plane of the subcommunicator; iteratively, beginning with a nodeone hop away from the lower right node in the negative direction of thefirst dimension until a node at a next hop away from the lower rightnode is not included in the subcommunicator: assigning a node at a nexthop away from the lower right node in the negative direction of thefirst dimension to be the lower left node of the logical plane of thesubcommunicator; and iteratively, beginning with a node one hop awayfrom the lower right node and a node one hop away from the lower leftnode in the positive direction of the second dimension until a node at anext hop away from the lower right or lower left node is not included inthe subcommunicator: assigning a node at a next hop away from the lowerright node in the positive direction of the second dimension to be theupper right node of the logical plane and assigning a node at a next hopaway from the lower left node in the positive direction of the seconddimension to be the upper left node of the logical plane.
 12. Theapparatus of claim 9, further comprising computer program instructionsthat, when executed, cause the apparatus to carry out the step ofconstructing a set of unique logical planes of the subcommunicator independence upon the logical planes established by each node.
 13. Theapparatus of claim 12, further comprising computer program instructionsthat, when executed, cause the apparatus to carry out the step of: uponconstructing the set of unique logical planes of the subcommunicator,performing data communications amongst the compute nodes of thesubcommunicator utilizing optimization techniques based on the topologyof the unique logical planes.
 14. The apparatus of claim 9, wherein atopology of the subcommunicator communicator comprises a torus networktopology comprising N-dimensions and N comprises an integer greater thanone.
 15. A computer program product for identifying a plurality oflogical planes formed of compute nodes of a subcommunicator in aparallel computer, the computer program product disposed upon a computerreadable medium, the computer program product comprising computerprogram instructions that, when executed, cause a computer to carry outthe steps of: for each compute node of the subcommunicator anditeratively, for a plurality of dimensions beginning with a firstdimension: establishing, by a plane building node, in a positivedirection of the first dimension, all logical planes that include theplane building node and compute nodes of the subcommunicator in apositive direction of a second dimension, wherein the second dimensionis orthogonal to the first dimension; and establishing, by the planebuilding node, in a negative direction of the first dimension, alllogical planes that include the plane building node and compute nodes ofthe subcommunicator in the positive direction of the second dimension.16. The computer program product of claim 15, wherein establishing, in apositive direction of the first dimension, all logical planes thatinclude the plane building node and compute nodes of the subcommunicatorin a positive direction of a second dimension, further comprises:assigning the plane building node to be the lower left node of a logicalplane of the subcommunicator; iteratively, beginning with a node one hopaway from the lower left node in a positive direction of the firstdimension until a node at a next hop away from the lower left node isnot included in the subcommunicator: assigning a node at a next hop awayfrom the lower left node in the positive direction of the firstdimension to be the lower right node of the logical plane of thesubcommunicator; and iteratively, beginning with nodes one hop away fromthe lower left node and lower right node in a positive direction of asecond dimension until a node at a next hop away from the lower left orlower right node is not included in the subcommunicator: assigning anode at a next hop away from the lower left node in the positivedirection of the second dimension to be the upper left node of thelogical plane and assigning a node at a next hop away from the lowerright node in the positive direction of the second dimension to be theupper right node of the logical plane.
 17. The computer program productof claim 15, wherein establishing, by the plane building node, in anegative direction of the first dimension, all logical planes thatinclude the plane building node and compute nodes of the subcommunicatorin the positive direction of the second dimension, further comprises:assigning the plane building node to be the lower right node of alogical plane of the subcommunicator; iteratively, beginning with a nodeone hop away from the lower right node in the negative direction of thefirst dimension until a node at a next hop away from the lower rightnode is not included in the subcommunicator: assigning a node at a nexthop away from the lower right node in the negative direction of thefirst dimension to be the lower left node of the logical plane of thesubcommunicator; and iteratively, beginning with a node one hop awayfrom the lower right node and a node one hop away from the lower leftnode in the positive direction of the second dimension until a node at anext hop away from the lower right or lower left node is not included inthe subcommunicator: assigning a node at a next hop away from the lowerright node in the positive direction of the second dimension to be theupper right node of the logical plane and assigning a node at a next hopaway from the lower left node in the positive direction of the seconddimension to be the upper left node of the logical plane.
 18. Thecomputer program product of claim 15, further comprising computerprogram instructions that, when executed, cause the computer to carryout the step of constructing a set of unique logical planes of thesubcommunicator in dependence upon the logical planes established byeach node.
 19. The computer program product of claim 18, furthercomprising computer program instructions that, when executed, cause thecomputer to carry out the step of: upon constructing the set of uniquelogical planes of the subcommunicator, performing data communicationsamongst the compute nodes of the subcommunicator utilizing optimizationtechniques based on the topology of the unique logical planes.
 20. Thecomputer program product of claim 15, wherein a topology of thesubcommunicator communicator comprises a torus network topologycomprising N-dimensions and N comprises an integer greater than one.